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In analogy to wavelet transforms, we use group-like structures in order to introduce a class of integral transformations. We consider them in the context of Hilbert spaces and study their inversion., This is the proceedings of the 2nd Japanese-German Symposium on Infinite Dimensional Harmonic Analysis held from September 20th to September 24th 1999 at the Department of Mathematics of Kyoto University., この論文集は, 1999年9月20日から9月24日の日程で京都大学理学研究科数学教室において開催された第2回日独セミナー「無限次元調和解祈」の成果をもとに編集されたものである., 編集 : ハーバート・ハイヤー, 平井 武, 尾畑 信明, Editors: Herbert Heyer, Takeshi Hirai, Nobuaki Obata #en

Emissions trading markets have been touted as the most efficient mechanism to achieve environmental goals at least cost. Whether in the form of voluntary markets or in a mandatory framework like in the first phase of the European Union (EU) Emission Trading Scheme (ETS), the regulator sets a cap on the emissions which can occur without penalty, and provides emissions allowances accordingly. The recipients are free to use these emission certificates to cover their emissions, or to sell them to the firms which are expected to emit more than what they can cover with their original allocations. As observed in most existing programs, cap-and-trade systems can fail to reach their emission targets as too generous an allocation of pollution permits serves as a disincentive for emissions reductions and deflates pollution prices. Moreover, the implementation of the first phase of the EU-ETS has been widely criticized on one more sensitive account: providing significant (some went as far as calling them obscene) windfall profits for power producers. Here we weight on this debate with the results of a rigorous quantitative modeling undertaking, providing insight into what went wrong in the first phase of the EU-ETS, and proposing alternative reduction schemes with provable advantages. Using market equilibrium models and numerical tools, we demonstrate that properly designed market-based pollution reduction mechanisms can reach pre-assigned emissions targets at low reduction cost and windfall profits, while being flexible enough to promote clean technologies. In the present article, we illustrate our claims with the results of a hypothetical cap-and-trade scheme for the Japanese electricity market.

In the Black-Scholes type financial market, the risky asset S 1 ( ) is supposed to satisfy dS 1 ( t ) = S 1 ( t )( b ( t ) dt + Sigma ( t ) dW ( t ) where W ( ) is a Brownian motion. The processes b ( ), Sigma ( ) are progressively measurable with respect to the filtration generated by W ( ). They are known as the mean rate of return and the volatility respectively. A portfolio is described by a progressively measurable processes Pi1 ( ), where Pi1 ( t ) gives the amount invested in the risky asset at the time t. Typically, the optimal portfolio Pi1 ( ) (that, which maximizes the expected utility), depends at the time t, among other quantities, on b ( t ) meaning that the mean rate of return shall be known in order to follow the optimal trading strategy. However, in a real-world market, no direct observation of this quantity is possible since the available information comes from the behavior of the stock prices which gives a noisy observation of b ( ). In the present work, we consider the optimal portfolio selection which uses only the observation of stock prices.